Admissions

CLD and CHD Dual Degree Programmes

Programs:

CLD, CHD

Admission:

Through entrance exam and interview

1. A student can apply for both CLD/CHD 2. Separate written test (entrance examinations) will be conducted for CLD and CHD 3. Written test + background will be used for screening. 4. Interview is the final decision.

Eligibility:

Stream1: Higher Secondary/class XII or equivalent in Science stream with Physics and Mathematics.

Stream2: Higher Secondary/class XII or equivalent in Humanities, Arts and Social Science with Mathematics.

For CLD program, a keen interest or work in languages and aptitude for for conceptual analysis and Mathematics is essential.

For EHD program, a keen interest or work in Arts, Humanities, Social Science and aptitude for logical analysis and Mathematics is essential.

UNIT I. RELATIONS AND FUNCTIONS 1. Relations and Functions: Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.UNIT-II: ALGEBRA1. Matrices: Concept, notation, order, equality, types of matrices, zero matrix,transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simpleproperties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).2. Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

UNIT-III: CALCULUS1. Continuity and Differentiability:

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function.Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations.2. Applications of Derivatives: Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).3. Integrals: Integration as inverse process of differentiation. Integration of a variaty of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.4. Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).5. Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx+ py = q, where p and q are functions of x.

UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY1. Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, arallel and collinear vectors), position vector of a point, negativeof a vector, components of a vector, addition of vectors, ultiplication of a vector by a scalar, position vector of a point ividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.2. Three - dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane.